Altermagnetism

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An example of an altermagnetic ordering, with the direction of the spins and the spatial orientation of the atoms alternating on the neighbouring sites in the crystal. Altermagnetism1.jpg
An example of an altermagnetic ordering, with the direction of the spins and the spatial orientation of the atoms alternating on the neighbouring sites in the crystal.

In condensed matter physics, altermagnetism is a type of persistent magnetic state in ideal crystals. [1] [2] [3] [4] [5] Altermagnetic structures are collinear and crystal-symmetry compensated, resulting in zero net magnetisation. [1] [5] [6] [7] Unlike in an ordinary collinear antiferromagnet, another magnetic state with zero net magnetization, the electronic bands in an altermagnet are not Kramers degenerate, but instead depend on the wavevector in a spin-dependent way. [1] Related to this feature, key experimental observations were published in 2024. [8] [9] It has been speculated that altermagnetism may have applications in the field of spintronics. [6] [10]

Contents

Crystal structure and symmetry

In altermagnetic materials, atoms form a regular pattern with alternating spin and spatial orientation at adjacent magnetic sites in the crystal. [5] [7]

Atoms with opposite magnetic moment are in altermagnets coupled by crystal rotation or mirror symmetry. [1] [5] [6] [7] [8] [9] The spatial orientation of magnetic atoms may originate from the surrounding cages of non-magnetic atoms. [7] [11] The opposite spin sublattices in altermagnetic manganese telluride (MnTe) are related by spin rotation combined with six-fold crystal rotation and half-unit cell translation. [7] [8] In altermagnetic ruthenium dioxide (RuO2), the opposite spin sublattices are related by four-fold crystal rotation. [7] [9]

Alternating magnetic and crystal pattern in altermagnetic manganese telluride (MnTe, left) and ruthenium dioxide (RuO2, right). Altermagnetism2.jpg
Alternating magnetic and crystal pattern in altermagnetic manganese telluride (MnTe, left) and ruthenium dioxide (RuO2, right).

Electronic structure

One of the distinctive features of altermagnets is a specifically spin-split band structure [7] which was first experimentally observed in work that was published in 2024. [8] Altermagnetic band structure breaks time-reversal symmetry, [7] [11] Eks=E-ks (E is energy, k wavevector and s spin) as in ferromagnets, however unlike in ferromagnets, it does not generate net magnetization. The altermagnetic spin polarisation alternates in wavevector space and forms characteristic 2, 4, or 6 spin-degenerate nodes, respectively, which correspond to d-, g, or i-wave order parameters. [7] A d-wave altermagnet can be regarded as the magnetic counterpart of a d-wave superconductor. [12]

The altermagnetic spin polarization in band structure (energy–wavevector diagram) is collinear and does not break inversion symmetry. [7] The altermagnetic spin splitting is even in wavector, i.e. (kx2-ky2)sz. [7] [8] It is thus also distinct from noncollinear Rasba or Dresselhaus spin texture which break inversion symmetry in noncentrosymmetric nonmagnetic or antiferromagnetic materials due to the spin-orbit coupling. Unconventional time-reversal symmetry breaking, giant ~1eV spin splitting and anomalous Hall effect was first theoretically predicted [11] and experimentally confirmed [13] in RuO2.

Materials

Direct experimental evidence of altermagnetic band structure in semiconducting MnTe and metallic RuO2 was first published in 2024. [8] [9] Many more materials are predicted to be altermagnets – ranging from insulators, semiconductors, and metals to superconductors. [6] [7] Altermagnetism was predicted in 3d and 2d materials [3] [6] with both light as well as heavy elements and can be found in nonrelativistic as well as relativistic band structures. [7] [8] [11]

Properties

Altermagnets exhibit an unusual combination of ferromagnetic and antiferromagnetic properties, and remarkably more closely resemble those of ferromagnets. [1] [5] [6] [7] Hallmarks of altermagnetic materials such as the anomalous Hall effect [11] have been observed before [13] [14] (but this effect occurs also in other magnetically compensated systems such as non-collinear antiferromagnets [15] ). Altermagnets also exhibit unique properties such as anomalous and spin currents that can change sign as the crystal rotates. [16]

Related Research Articles

<span class="mw-page-title-main">Condensed matter physics</span> Branch of physics

Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases that arise from electromagnetic forces between atoms and electrons. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the superconducting phase exhibited by certain materials at extremely low cryogenic temperatures, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, the Bose–Einstein condensates found in ultracold atomic systems, and liquid crystals. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other physics theories to develop mathematical models and predict the properties of extremely large groups of atoms.

Magnetoresistance is the tendency of a material to change the value of its electrical resistance in an externally-applied magnetic field. There are a variety of effects that can be called magnetoresistance. Some occur in bulk non-magnetic metals and semiconductors, such as geometrical magnetoresistance, Shubnikov–de Haas oscillations, or the common positive magnetoresistance in metals. Other effects occur in magnetic metals, such as negative magnetoresistance in ferromagnets or anisotropic magnetoresistance (AMR). Finally, in multicomponent or multilayer systems, giant magnetoresistance (GMR), tunnel magnetoresistance (TMR), colossal magnetoresistance (CMR), and extraordinary magnetoresistance (EMR) can be observed.

Spintronics, also known as spin electronics, is the study of the intrinsic spin of the electron and its associated magnetic moment, in addition to its fundamental electronic charge, in solid-state devices. The field of spintronics concerns spin-charge coupling in metallic systems; the analogous effects in insulators fall into the field of multiferroics.

<span class="mw-page-title-main">Magnon</span> Spin 1 quasiparticle; quantum of a spin wave

A magnon is a quasiparticle, a collective excitation of the spin structure of an electron in a crystal lattice. In the equivalent wave picture of quantum mechanics, a magnon can be viewed as a quantized spin wave. Magnons carry a fixed amount of energy and lattice momentum, and are spin-1, indicating they obey boson behavior.

Multiferroics are defined as materials that exhibit more than one of the primary ferroic properties in the same phase:

Exchange bias or exchange anisotropy occurs in bilayers of magnetic materials where the hard magnetization behavior of an antiferromagnetic thin film causes a shift in the soft magnetization curve of a ferromagnetic film. The exchange bias phenomenon is of tremendous utility in magnetic recording, where it is used to pin the state of the readback heads of hard disk drives at exactly their point of maximum sensitivity; hence the term "bias."

<span class="mw-page-title-main">Topological order</span> Type of order at absolute zero

In physics, topological order is a kind of order in the zero-temperature phase of matter. Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states. Microscopically, topological orders correspond to patterns of long-range quantum entanglement. States with different topological orders cannot change into each other without a phase transition.

<span class="mw-page-title-main">Spin density wave</span>

Spin-density wave (SDW) and charge-density wave (CDW) are names for two similar low-energy ordered states of solids. Both these states occur at low temperature in anisotropic, low-dimensional materials or in metals that have high densities of states at the Fermi level . Other low-temperature ground states that occur in such materials are superconductivity, ferromagnetism and antiferromagnetism. The transition to the ordered states is driven by the condensation energy which is approximately where is the magnitude of the energy gap opened by the transition.

Spin pumping is the dynamical generation of pure spin current by the coherent precession of magnetic moments, which can efficiently inject spin from a magnetic material into an adjacent non-magnetic material. The non-magnetic material usually hosts the spin Hall effect that can convert the injected spin current into a charge voltage easy to detect. A spin pumping experiment typically requires electromagnetic irradiation to induce magnetic resonance, which converts energy and angular momenta from electromagnetic waves to magnetic dynamics and then to electrons, enabling the electronic detection of electromagnetic waves. The device operation of spin pumping can be regarded as the spintronic analog of a battery.

The spin Hall effect (SHE) is a transport phenomenon predicted by Russian physicists Mikhail I. Dyakonov and Vladimir I. Perel in 1971. It consists of the appearance of spin accumulation on the lateral surfaces of an electric current-carrying sample, the signs of the spin directions being opposite on the opposing boundaries. In a cylindrical wire, the current-induced surface spins will wind around the wire. When the current direction is reversed, the directions of spin orientation is also reversed.

Gallium manganese arsenide, chemical formula (Ga,Mn)As is a magnetic semiconductor. It is based on the world's second most commonly used semiconductor, gallium arsenide,, and readily compatible with existing semiconductor technologies. Differently from other dilute magnetic semiconductors, such as the majority of those based on II-VI semiconductors, it is not paramagnetic but ferromagnetic, and hence exhibits hysteretic magnetization behavior. This memory effect is of importance for the creation of persistent devices. In (Ga,Mn)As, the manganese atoms provide a magnetic moment, and each also acts as an acceptor, making it a p-type material. The presence of carriers allows the material to be used for spin-polarized currents. In contrast, many other ferromagnetic magnetic semiconductors are strongly insulating and so do not possess free carriers. (Ga,Mn)As is therefore a candidate material for spintronic devices but it is likely to remain only a testbed for basic research as its Curie temperature could only be raised up to approximatelly 200 K.

<span class="mw-page-title-main">Magnetic structure</span> Ordered arrangement of magnetic spins in a material

The term magnetic structure of a material pertains to the ordered arrangement of magnetic spins, typically within an ordered crystallographic lattice. Its study is a branch of solid-state physics.

<span class="mw-page-title-main">Superexchange</span> Strong coupling between two cations through an intermediary anion

Superexchange or Kramers–Anderson superexchange interaction, is a prototypical indirect exchange coupling between neighboring magnetic moments by virtue of exchanging electrons through a non-magnetic anion known as the superexchange center. In this way, it differs from direct exchange, in which there is direct overlap of electron wave function from nearest neighboring cations not involving an intermediary anion or exchange center. While direct exchange can be either ferromagnetic or antiferromagnetic, the superexchange interaction is usually antiferromagnetic, preferring opposite alignment of the connected magnetic moments. Similar to the direct exchange, superexchange calls for the combined effect of Pauli exclusion principle and Coulomb's repulsion of the electrons. If the superexchange center and the magnetic moments it connects to are non-collinear, namely the atomic bonds are canted, the superexchange will be accompanied by the antisymmetric exchange known as the Dzyaloshinskii–Moriya interaction, which prefers orthogonal alignment of neighboring magnetic moments. In this situation, the symmetric and antisymmetric contributions compete with each other and can result in versatile magnetic spin textures such as magnetic skyrmions.

The quantum rotor model is a mathematical model for a quantum system. It can be visualized as an array of rotating electrons which behave as rigid rotors that interact through short-range dipole-dipole magnetic forces originating from their magnetic dipole moments. The model differs from similar spin-models such as the Ising model and the Heisenberg model in that it includes a term analogous to kinetic energy.

In condensed matter physics, a quantum spin liquid is a phase of matter that can be formed by interacting quantum spins in certain magnetic materials. Quantum spin liquids (QSL) are generally characterized by their long-range quantum entanglement, fractionalized excitations, and absence of ordinary magnetic order.

<span class="mw-page-title-main">Antisymmetric exchange</span> Contribution to magnetic exchange interaction

In Physics, antisymmetric exchange, also known as the Dzyaloshinskii–Moriya interaction (DMI), is a contribution to the total magnetic exchange interaction between two neighboring magnetic spins, and . Quantitatively, it is a term in the Hamiltonian which can be written as

In solid-state physics, the kagome metal or kagome magnet is a type of ferromagnetic quantum material. The atomic lattice in a kagome magnet has layered overlapping triangles and large hexagonal voids, akin to the kagome pattern in traditional Japanese basket-weaving. This geometry induces a flat electronic band structure with Dirac crossings, in which the low-energy electron dynamics correlate strongly.

Magnetic 2D materials or magnetic van der Waals materials are two-dimensional materials that display ordered magnetic properties such as antiferromagnetism or ferromagnetism. After the discovery of graphene in 2004, the family of 2D materials has grown rapidly. There have since been reports of several related materials, all except for magnetic materials. But since 2016 there have been numerous reports of 2D magnetic materials that can be exfoliated with ease just like graphene.

<span class="mw-page-title-main">Gang Cao</span> American physicist

Gang Cao is an American condensed matter physicist, academic, author, and researcher. He is a professor of physics at the University of Colorado Boulder. and Director of Center for Experiments on Quantum Materials.

References

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  2. ↑ Mazin, Igor (2024-01-08). "Altermagnetism Then and Now". Physics. 17: 4. arXiv: 2105.05820 . doi:10.1103/PhysRevX.12.031042.
  3. 1 2 Mazin, Igor; González-Hernández, Rafael; Šmejkal, Libor (2023-09-05), Induced Monolayer Altermagnetism in MnP(S,Se)$_3$ and FeSe, arXiv: 2309.02355 , retrieved 2024-02-15
  4. ↑ Wilkins, Alex (14 February 2024). "The existence of a new kind of magnetism has been confirmed". New Scientist. Retrieved 2024-02-15.
  5. 1 2 3 4 5 Savitsky, Zack. "Researchers discover new kind of magnetism". Science.org. Retrieved 16 February 2024.
  6. 1 2 3 4 5 6 Šmejkal, Libor; Sinova, Jairo; Jungwirth, Tomas (2022-12-08). "Emerging Research Landscape of Altermagnetism". Physical Review X. 12 (4): 040501. arXiv: 2204.10844 . Bibcode:2022PhRvX..12d0501S. doi:10.1103/PhysRevX.12.040501.
  7. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Šmejkal, Libor; Sinova, Jairo; Jungwirth, Tomas (2022-09-23). "Altermagnetism: spin-momentum locked phase protected by non-relativistic symmetries". Physical Review X. 12 (3): 031042. arXiv: 2105.05820 . doi:10.1103/PhysRevX.12.031042. ISSN   2160-3308.
  8. 1 2 3 4 5 6 7 Krempaský, J.; Šmejkal, L.; D’Souza, S. W.; Hajlaoui, M.; Springholz, G.; Uhlířová, K.; Alarab, F.; Constantinou, P. C.; Strocov, V.; Usanov, D.; Pudelko, W. R.; González-Hernández, R.; Birk Hellenes, A.; Jansa, Z.; Reichlová, H. (February 2024). "Altermagnetic lifting of Kramers spin degeneracy". Nature. 626 (7999): 517–522. arXiv: 2308.10681 . doi:10.1038/s41586-023-06907-7. ISSN   1476-4687. PMID   38356066.
  9. 1 2 3 4 Fedchenko, Olena; Minár, Jan; Akashdeep, Akashdeep; D’Souza, Sunil Wilfred; Vasilyev, Dmitry; Tkach, Olena; Odenbreit, Lukas; Nguyen, Quynh; Kutnyakhov, Dmytro; Wind, Nils; Wenthaus, Lukas; Scholz, Markus; Rossnagel, Kai; Hoesch, Moritz; Aeschlimann, Martin (2024-02-02). "Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO 2". Science Advances. 10 (5): eadj4883. doi:10.1126/sciadv.adj4883. ISSN   2375-2548. PMC   10830110 . PMID   38295181.
  10. ↑ "Altermagnetism proves its place on the magnetic family tree". ScienceDaily. Retrieved 2024-02-15.
  11. 1 2 3 4 5 Šmejkal, Libor; González-Hernández, Rafael; Jungwirth, T.; Sinova, J. (5 June 2020). "Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets". Science Advances. 6 (23). arXiv: 1901.00445 . doi:10.1126/sciadv.aaz8809.
  12. ↑ Šmejkal, Libor; Sinova, Jairo; Jungwirth, Tomas (2022-09-23). "Beyond Conventional Ferromagnetism and Antiferromagnetism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry". Physical Review X. 12 (3): 031042. arXiv: 2105.05820 . doi:10.1103/PhysRevX.12.031042.
  13. 1 2 Feng, Zexin; Zhou, Xiaorong; Šmejkal, Libor; Wu, Lei; Zhu, Zengwei; Guo, Huixin; González-Hernández, Rafael; Wang, Xiaoning; Yan, Han; Qin, Peixin; Zhang, Xin; Wu, Haojiang; Chen, Hongyu; Meng, Ziang; Liu, Li; Xia, Zhengcai; Sinova, Jairo; Jungwirth, Tomáš; Liu, Zhiqi (7 November 2022). "An anomalous Hall effect in altermagnetic ruthenium dioxide". Nature Electronics. 5 (11): 735–743. arXiv: 2002.08712 . doi:10.1038/s41928-022-00866-z.
  14. ↑ Gonzalez Betancourt, R. D.; Zubáč, J.; Gonzalez-Hernandez, R.; Geishendorf, K.; Šobáň, Z.; Springholz, G.; Olejník, K.; Šmejkal, L.; Sinova, J.; Jungwirth, T.; Goennenwein, S. T. B.; Thomas, A.; Reichlová, H.; Železný, J.; Kriegner, D. (20 January 2023). "Spontaneous Anomalous Hall Effect Arising from an Unconventional Compensated Magnetic Phase in a Semiconductor". Physical Review Letters. 130 (3). arXiv: 2112.06805 . doi:10.1103/PhysRevLett.130.036702.
  15. ↑ Nakatsuji, Satoru; Kiyohara, Naoki; Higo, Tomoya (November 2015). "Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature". Nature. 527 (7577): 212–215. doi:10.1038/nature15723.
  16. ↑ Gonzalez Betancourt, R. D.; <C5><A0>mejkal, Libor; Vyborny, Karel; Yahagi, Yuta; Sinova, Jairo; Jungwirth, Tomas; Zelezny, Jakub (2021-03-26). "Efficient Electrical Spin Splitter Based on Nonrelativistic Collinear Antiferromagnetism". Physical Review Letters. 126: 127701. arXiv: 2002.07073 . doi:10.1103/PhysRevLett.126.127701.{{cite journal}}: CS1 maint: numeric names: authors list (link)
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